That works fine as you wrote it. You have to be careful when there are negative numbers insider the square roots. Then the law allowing radicands to be separated no longer apply.
–
Ron GordonJan 11 '13 at 23:12

3 Answers
3

Your work is just fine: you've shown you know that $\dfrac 12 = \sqrt{\dfrac{1}{4}},\;\;$ and that for any $x,y\in \mathbb{R^+\cup \{0\}},\;\;\sqrt x \cdot \sqrt y=\sqrt{xy}$.

The negative sign outside of the radicand has no impact on your operations: since the operations between terms is strictly multiplication, we can operate (multiply) as if the positive terms are entirely contained within parentheses, all of which is then multiplied by $-1$:

What you wrote is correct because $\sqrt{\frac{1}{4}}=\frac{1}{2}$ and for any $x,y\in \mathbb{R^+_0}$, $\sqrt x \sqrt y=\sqrt{xy}$. The minus sign (which is just multiplying by $-1)$ has no influence on the computation because you followed this rule.